Free fall from unknown height

Data
g = 9.8 m/s²
t = 8 s

Resolution
By applying the formula of velocity in free fall, we get that:

$$\begin{gathered} v=-g·t \Rightarrow \\ v = -9.8 m/s^{\cancel{2}} · 8 \cancel{s} \Rightarrow \\ \boxed{v= -78.4 m/s} \end{gathered}$$

To find out the distance traveled, we must calculate the displacement of the stone (Δy). This displacement is calculated by subtracting the position after 8 second (y8) from the position at the time 0 (y0). If we develop the equations of the position in both cases:

$$\begin{gathered} \Delta y = y_8-y_0 =H-\frac{1}{2}·g·{t_8}^2 - \left(H-\frac{1}{2}·g·{t_0}^2\right) \Rightarrow \\ \Delta y =H-\frac{1}{2}·g·8^2 - \left(H-\cancel{\frac{1}{2}·g·8^2}\right) \Rightarrow \\ \Delta y =\cancel{H}-\frac{1}{2}·9.8·8^2 -\cancel{H \Rightarrow } \\ \boxed{\Delta y = 313.6 m} \end{gathered}$$